well skill depends usually what you have lead in war, so a US admiral who lead a CV division for almost a year should be definately better than a german admiral supervising a shipyard. besides the skills, there are some traits which should be implemented like "Carrier Leader" or "Cavalry officer" - this would make the game a bit less germano-centric maybe and support the naval powers.
New traits would indeed be nice but I'm not sure if the engine can handle them. The traits which benefit battle events have already very high numbers. Such a system might have a natural upper limit. But more and - finally - fully moddable traits would be really nice to have.
The skill of the Admiral commanding some CVs for a year should be reviewed in the light of his next commands. If he was sent to command a shipyard afterwards, he might not have been as good as expected.
It's not so easy.
air force
ENG/USA/GER > JAP/SOV > ITA/FRA
well, Luftwaffe was an offensive arm mostly used for air supporting the army and this is can be modelled in removing superior tacticians traits and carpet bomber traits entirely (eg Klepke) - the ST traits: those can come later when germany was historically attacked by UK and USA.
so i wouldnt say that Luftwaffe was superior to RAF in organization, structure and especially production. not even the same for fighters/interceptors and if you count the BoB as a decisive battle in.
Don't misunderstand me: the ranking shouldn't be read as superb / mediocre / abysmal. Just the opposite, the differences in leadership should be not as great as your original 4 quality levels indicate; your approach is just too simplistic. The ranking should be read as 'above average / average / below average'. The average (air) leader skills might more be like 2.0 / 1.7 / 1.5. Tbh air leader skills are somewhat exaggerated, they'd be reduced. Skill 4 should be totally avoided - an exception might be Dowding
removing superior tacticians: you're kidding, are you?
removing carpet bomber: find the leaders who actually did the Coventry bombing, the Baedecker raids or the V1/V2 bombardment in the west or the strategic bombing runs on the eastern front. They're very few but only these qualify for this special trait.
Klepke;926;GER;1935;1937;1939;1990;1;6;4096;3;0;5;2;Klepke_Waldemar_ger;1930;1943;x
No frontline command, but he served as an instructor at the War Academy and as commander of the flight training units.
Klepke;926;GER;1935;1937;1939;1990;1;6;0;1;0;5;2;Klepke_Waldemar_ger;1930;1947;x #*1882
nah nah i'm not a masochist. Lütjens and Marschal will still be good leaders and Dönitz, Friedeburg as well. just i think if Raeder is rated like Nimitz and Yamamoto or Fechteler weaker than Boehm than something is wrong.
just as you mentioned it, if you fire up your game with this CSV, ai ignores Raeder completely and Marschal is in command of the Kriegsmarine main fleet.
Nimitz;60448;USA;1930;1938;1941;1944;0;9;12288;5;0;5;1;L60448;1930;1947;x
Yamamoto I.;101296;JAP;1930;1930;1937;1939;0;7;12288;5;0;5;1;L101296;1930;1990;x
Raeder;409;GER;1930;1930;1930;1936;0;9;4096;4;0;4;1;L409;1930;1960;x #Arma
Raeder;409;GER;1930;1930;1930;1936;0;9;4096;4;0;5;1;Raeder_Erich1_ger;1930;1960;x #vanilla
Raeder;409;GER;1922;1925;1928;1939;0;9;4096;4;0;5;1;Raeder8_colour_ger;1922;1943;x #v25
re Raeder: I don't know why do you think he's rated like Nimitz and Yamamoto. He was never as good as Dönitz. But you'd keep in mind that he was in von Hipper's staff and 'participated' in all major naval battles including Dogger Bank and Jutland. That should have given him some insights.
Raeder;409;GER;1922;1925;1928;1939;0;9;4096;3;0;5;1;Raeder8_colour_ger;1922;1943;x #*1876